Voronoi of packing

Hello,

I was wondering if somone can help me create a definition that does the following:

I want to pack a given volume with spheres.

In order to do some experimentation it should be possible to alter the shape of the volume

(though this does not have to be part of the grasshopper definition)

The diameter of the spheres should be irregular and random (but I want to be able to determine the upper and lower bound).

Next, I want to create voronoi cells based on this sphere packing.

Some examples are given here:

http://bazantgroup.mit.edu/img-movies/images&movies/voronoi3.jpg

http://math.lbl.gov/voro++/examples/custom_output/custom_output_l.png

http://math.lbl.gov/voro++/examples/irregular/irregular_l.png

https://www.youtube.com/watch?v=NjKhpJBR6oI

Or a particularly good example is:

http://www.evolo.us/architecture/voronoi-skyscraper/

The project is (unfortunately) very similar to this over here. I too like the final boundary to be a bit random like in the example.

Next I want to connect the centres of every sphere to the centre of every immediately adjacent sphere (and only to the immediately adjacent spheres)

The goal is to create a second random network based on the first one, so that the two networks are intertwined but not intersecting.

In a later stage of the project I want to give some thickness to the connection lines and make them into paths / stairs.

Kind regards,

Jeffrey Kim

Replies to This Discussion

Permalink Reply by Mateusz Zwierzycki on May 8, 2012 at 7:46pm

well, sphere and circle packing is really awesome subject to talk about, but i dont think its necessary for your purpose...

http://storage.ning.com/topology/rest/1.0/file/get/2768717361?profi...

(this image comes from discussion : http://www.grasshopper3d.com/forum/topics/skeletal-mesh )

so as you can see your aim : "The goal is to create a second random network based on the first one, so that the two networks are intertwined but not intersecting." doesnt need to come directly from sphere packing - in 3 dimensional space, dual of voronoi edges is 3d delaunay triangulation, you can find some clues how to achieve it in that discussion....

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other approach which comes to my mind now, is kangaroo-based :

http://www.grasshopper3d.com/video/clustering-1

Permalink Reply by Jeffrey Kim on May 9, 2012 at 9:38pm

Thank you for your response. There is one concern i have: the sphere packing would ensure a certain distance between the points (determined by the radiii of the spheres) which would make the distribution of the points in the space a bit different from a completely random distribution of the points in the space. Is it possible to set a minimum distance between the points when placing them randomly within a space? The purpose of the spherpacking was to create "voids" of a certain volume in the structure. Is it possible to achieve the same result without the sphere packing?

Permalink Reply by Mateusz Zwierzycki on May 10, 2012 at 7:18am

Its possible, and quite easy - generate random point, for each find it nearest neighbour, and delete if its closer than minimal value. But that would not generate nice packing, where spheres are "touching" more than one neighbour.... and so, if you would use this points to generate 3d voronoi, then it would not be so "uniform"

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